A silage cutting head for cutting silage from a heap (23) has a linear silage cutter (26) bounding a longitudinal side of an entry passage (127) for allowing silage cut off the heap to pass through. An outlet passage (29) of the cutting head has a width in longitudinal direction of the entry passage, which is smaller than the width of the entry passage. The cutting head further has a conveyor screw (30) for laterally transporting cut silage from a side zone of the cutting head towards the outlet passage (29) and one or more rotatable side cutters (141). A guide surface (164) extends around a portion of the conveyor screw and ends laterally inwardly and closely adjacent rotary contour or contours of the side cutter or side cutters. The rotary contour or contours of the side cutter or side cutters project radially beyond at least a portion of the guide surface.